applied sciences

Article

Secrecy Energy Efficiency Maximization inan Underlying Cognitive Radio–NOMA System witha Cooperative Relay and an Energy-Harvesting User

Carla E. Garcia , Mario R. Camana and Insoo Koo *

School of Electrical and Computer Engineering, University of Ulsan, Ulsan 680-749, Korea;carli.garcia27@hotmail.com (C.E.G.); mario_camana@hotmail.com (M.R.C.)* Correspondence: iskoo@ulsan.ac.kr; Tel.: +82-52-259-1429

Received: 8 April 2020; Accepted: 21 May 2020; Published: 24 May 2020�����������������

Abstract: Security is considered a critical issue in the deployment of 5G networks because of thevulnerability of information that can be intercepted by eavesdroppers in wireless transmissionenvironments. Thus, physical layer security has emerged as an alternative for the secure enablingof 5G technologies and for tackling this security issue. In this paper, we study the secrecyenergy efficiency (SEE) in a downlink underlying cognitive radio (CR)—non-orthogonal multipleaccess (NOMA) system with a cooperative relay. The system has an energy-harvesting (EH)user and an eavesdropper, where the transmitter provides direct communication with a closesecondary user and a distant secondary user via the relay. Our objective is to maximize theSEE of the CR-NOMA system under the constraints of a minimum information rate for thesecondary users, a minimum amount of energy harvested by the EH user, and maximum poweravailability at the transmitter and the relay that still prevents them from causing unacceptableinterference with the primary user. The proposed solution to maximize the SEE is based onthe low-computational—complexity particle swarm optimization (PSO) algorithm. For validationpurposes, we compare the optimization outcomes obtained by the PSO algorithm with the optimalexhaustive search method. Furthermore, we compare the performance of our proposed CR-NOMAscheme with the conventional orthogonal multiple access (OMA) scheme.

Keywords: secrecy energy efficiency; 5G networks; cognitive radio; non-orthogonal multiple access(NOMA); particle swarm optimization (PSO)

1. Introduction

The rapid expansion of wireless networks has produced a massive increment in data traffic.The fundamental requirements for future networks such as 5G include massive connectivity ofusers and the Internet of Things (IoT), low latency, high energy efficiency, and higher data rates.Non-orthogonal multiple access (NOMA) has attracted extensive attention in the literature because itcan provide superior energy efficiency, higher data rates, and low transmission latency [1,2]. NOMA isbased on superposition coding at the transmitter and successive interference cancellation (SIC) at thereceiver, where multiple users can simultaneously access the same frequency with different transmitpower levels [3,4]. To further improve the coverage of the network, cooperative communications utilizea relay or a cooperative user to forward messages to the intended users who are very far away fromthe base station (BS) and who do not have a direct link because of obstacles or the shadowing effect.

Security represents one of the major problems in wireless networks because the signals transmittedcan be intercepted in the shared wireless medium. Physical layer security (PLS) was introduced tocomplement traditional security techniques, and it exploits the nature of physical layer dynamics

Appl. Sci. 2020, 10, 3630; doi:10.3390/app10103630 www.mdpi.com/journal/applsci

Appl. Sci. 2020, 10, 3630 2 of 15

to provide a secure transmission [5]. Several studies in the literature have investigated the securityin NOMA systems with the objectives of secrecy sum rate maximization [6–8] and secrecy energyefficiency (SEE) [3,9]. Zhang et al. [6] considered a single-input single-output NOMA system witha passive eavesdropper, where the objective was to maximize the secrecy sum rate (SSR) under theconstraint of minimum data rate at the users. The authors compared their proposed solution withthe orthogonal multiple access (OMA) method, obtaining a significant improvement of the SRR byusing NOMA. A downlink simultaneous wireless information and power transfer (SWIPT) systemwith NOMA was proposed in [7]. The BS simultaneously served several information receiversand multiple EH receivers in which the EH receivers were considered potential eavesdroppers.The authors solved the SSR maximization problem under the constraints of minimum data rate requiredby the information receiver users and minimum harvested energy required by the EH receivers.Garcia et al. [8] proposed secrecy sum rate maximization in a cooperative NOMA system composedof two users and a relay. The paper highlights the importance in cooperative communications ofimproving the secrecy performance of the network, since simulation results showed that highervalues for the secrecy sum rate were obtained by employing a cooperative relay compared to valuesobtained by the NOMA network without cooperative relaying. A cooperative system model withSWIPT was proposed in [10], where an EH user co-existed with a nearby user that applies SWIPTto harvest energy and work as a relay to help and guarantee a minimum data rate at the far user.The minimum transmit power problem was considered under the constraints of minimum signalto interference plus noise ratio (SINR) of the users and minimum harvested energy at the EH user.Mao et al. [11] considered an underlay cognitive multiple-input single-output NOMA system withSWIPT in which the secondary BS and the multiple secondary SWIPT users co-existed with severalprimary users via the underlay scheme. The minimum transmit power problem is investigated subjectto the constraints of minimum SINR, minimum energy harvested to satisfy the power consumption atthe users, and maximum interference power with the primary network.

Yao et al. [9] considered a downlink NOMA system composed of a BS and multiple legitime usersunder the presence of an eavesdropper. The Secrecy energy efficiency was maximized subject to theconstraints of minimum data rate and maximum available power at the BS. A NOMA cognitive radio(CR) system with energy harvesting (EH) users was proposed by Wang et al. [3] in which the secondaryusers harvest energy in the first phase and transmit their uplink information with NOMA in the secondphase under the presence of the eavesdropper. The authors proposed the secrecy energy efficiency(SEE) maximization problem under the constraints of minimum data rate, maximum interferencepower to the primary users (PUs) and maximum secrecy outage probability. However, none of theresearchers studied SEE maximization in a downlink CR-NOMA system with cooperative relayingand an EH user. The importance of the EH user lies in powering the user terminal expected in 5Gapplications, such as those in the Internet of Things (IoT) [12]. In this paper, we consider the EH userto be a receiver that stores energy from RF signals.

With the above motivations, and because energy efficiency is a crucial factor for future wirelessnetworks, we investigate a downlink CR-NOMA scheme to maximize the SEE with cooperativerelaying, subject to quality of service (QoS) requirements. We propose a particle swarm optimization(PSO)-based algorithm to solve the optimization problem, which has advantages over the optimalexhaustive search method, such as low computational complexity and high accuracy. Moreover, in theliterature, application of PSO in wireless communications networks has shown high performance inresolving optimization problems [8,13].

The main contributions of this paper are summarized as follows.

• Since we focus on enhancing the PLS (and to enable sustainable 5G networks), we proposemaximizing the SEE of the CR-NOMA system with cooperative relaying and an EH user toprevent eavesdropper wiretaps by satisfying the following QoS requirements: minimum requiredenergy at the EH user, a minimum data rate for secondary users, the maximum permissibletransmission power at the relay, and a transmitter that avoids interference with the primary user.

Appl. Sci. 2020, 10, 3630 3 of 15

• To reduce the computation complexity of the solution, we solve the SEE maximization problemwith a PSO-based algorithm that provides high-accuracy outcomes and high convergencespeed. In addition, we provide the mathematical boundaries for the variables of the proposedoptimization problem. The simulation results show that the proposed PSO algorithm achievesoutcomes very close to values obtained by the high computational–complexity exhaustivesearch method.

• We solve the SEE maximization problem for a CR orthogonal multiple access (CR-OMA) schemeto compare it with our proposed CR-NOMA scheme. Similar to the CR-NOMA system, we alsooptimize the power allocation variables of each OMA user. Simulation results show that ourproposed scheme based on NOMA outperforms the OMA scheme, where an improvement in theSEE of around 40% to more than 100% is achieved by NOMA compared with OMA .

The rest of this paper is organized as follows. The CR-NOMA network model with an EH user isdescribed in Section 2. In Section 3, the SEE maximization problem in the CR-NOMA networkis formulated, and the PSO-based power allocation scheme for SEE maximization is described.The comparison approach of SEE maximization in the CR-OMA scheme is studied in Section 4.Simulation results of the cooperative CR-NOMA network with an EH user are presented in Section 5.Finally, the conclusion is presented in Section 6. Table 1 lists the main abbreviations used throughoutthe paper.

Table 1. Nomenclature.

Abbreviation Term Abbreviation Term

NOMA non-orthogonal multiple access PSO particle swarm optimizationOMA orthogonal multiple access QoS quality of serviceSIC successive interference cancellation TDMA time-division multiple accessPLS physical layer security U1 nearby secondary userSEE secrecy energy efficiency U2 distant secondary user

2. Network Model

We study a downlink underlying CR-NOMA system consisting of one secondary transmitter,one cooperative relay, two secondary users, one EH user, one primary user and one eavesdropper.The cooperative relay operates in half-duplex mode and implements the decode-and-forward (DF)protocol. Figure 1 illustrates the system model; the nearby secondary user is U1, and we assume there isno direct link between the transmitter and the distant secondary user, U2, because of path obstruction.User 3 (denoted as U3) is the EH user and the primary user is denoted as PU. The system modelinvolves two phases. In Phase 1, the transmitter serves the secondary users and sends a superimposedsignal, x, composed of Message 1, Message 2, and Message 3 corresponding to the close, distant andEH users’ messages, respectively. Then, U1 and the relay receive the messages. In Phase 2, the relayretransmits Message 2 to U2 and U1. In the following, we provide a detailed description of thetwo phases.

Concerning Phase 1, let x1, x2 ∈ C denote the messages for U1 and U2, with transmit powers ofp1 and p2 respectively. According to the NOMA concept, the transmission power level for the userwith the lower channel gain should be higher than the transmission power level of the user withthe higher channel gain. Therefore, we consider p2 > p1. The energy signal intended for the EHuser, x3, can be a signal known to both secondary users prior to information transmission. At thesecondary transmitter, x3 is sent with a transmit power of p3. Then, the transmit signal is defined asx =√

p1x1 +√

p2x2 +√

p3x3. The channels from the transmitter to User 1, User 3, the relay, and theeavesdropper are denoted as h̃Tu1 , h̃Tu3, h̃TR and h̃TE, respectively. The channels from the relay to User1, User 2, and the eavesdropper are denoted as g̃Ru1 , g̃Ru2 , and g̃RE, respectively. We assume that thevariance in the noise of the users, the relay, and the eavesdropper is the same, and we define them as

Appl. Sci. 2020, 10, 3630 4 of 15

σ2 = σ2R = σ2

Ev = σ2u1

= σ2u2

. We also assume that U1 and U2 can cancel the interference from knownsymbol x3.

Figure 1. Underlying CR-NOMA system with a cooperative relay and an EH user.

In Phase 1, since the relay decodes Message 2 (considering Message 1 as interference), the rate ofMessage 2 at the relay is given by

Rx2,TR =12

log2(1 +p2hTR

p1hTR + σ2R), (1)

where hTR =∣∣h̃TR

∣∣2.At the eavesdropper, the rate of Message 1 is:

Rx1,TE =12

log2(1 +p1hTE

p2hTE + p3hTE + σ2Ev

), (2)

where hTE =∣∣h̃TE

∣∣2.The energy harvested by User 3 in Phase 1 can be expressed as

E(1)3 =

∣∣h̃Tu3∣∣2 (p1 + p2 + p3) τ =

hTu3(

p1 + p2 + p3)

2, (3)

where hTu3 =∣∣h̃Tu3

∣∣2, τ ∈ (0, 1), τ = 12 is the transmission time fraction for Phase 1.

In Phase 2, the relay retransmits Message 2. User 1 and the eavesdropper use maximum-ratiocombining, and the rate of Message 2 at U1 is given as follows:

Rx2,u1 =12

log2(1 +p2hTu1

p1hTu1+ σ2

u1

+prgRu1

σ2u1

), (4)

where hTu1=∣∣∣h̃Tu1

∣∣∣2, gRu1=∣∣∣g̃Ru1

∣∣∣2, and pr denotes the transmit power of Message 2 at the relay.The rate of Message 2 at the eavesdropper is given as follows:

Rx2,E =12

log2(1 +p2hTE

p1hTE + p3hTE + σ2E+

prgREσ2

E), (5)

Appl. Sci. 2020, 10, 3630 5 of 15

where gRE = |g̃RE|2.

Under NOMA, User 1 performs successive interference cancellation to remove the interference ofMessage 2, and decodes Message 1. Then, the rate of Message 1 at U1 is defined as follows:

Rx1,Tu1 =12

log2(1 +p1hTu1

σ2u1

). (6)

Therefore, the secrecy rate of Message 1 is given by

Ru1 =[Rx1,Tu1 − Rx1,TE

]+, (7)

where [c]+ = max (0, c).The rate of Message 2 at U2 is as follows:

Rx2,Ru2 =12

log2(1 +prgRu2

σ2u2

), (8)

where gRu2=∣∣∣g̃Ru2

∣∣∣2.The achievable rate of Message 2 is defined by the rate observed at U1, the relay, and User 2

as follows:Ru2,min = min(Rx2,u1 , Rx2,TR, Rx2,Ru2). (9)

Consequently, the secrecy rate of Message 2 is defined as:

Ru2 =[Ru2,min − Rx2,E

]+. (10)

The power at the transmitter and the relay should remain at a controllable level to avoidinterference with the primary user, and these power constraints are specified in Section 3.

3. Problem Formulation and the PSO-Based Power Allocation Scheme for SEE Maximization

The objective is to maximize the SEE, subject to the constraints of a minimum required rate at eachsecondary user, minimum energy harvested by U3, and maximum available power at the relay andtransmitter based on the maximum permissible interference with the primary user. The SEE is definedas the ratio of secrecy sum rate maximization to total power consumption [3,5,14]. The optimizationproblem can be modeled as follows:

maxp1,p2,p3,pr

Ru1 + Ru212 (p1 + p2 + p3 + pcT) +

12 (pr + pcR)

(11a)

s.t. Rx1,Tu1 ≥ φ1, (11b)

Ru2,min ≥ φ2, (11c)

p1 + p2 + p3 ≤ PmaxT , (11d)

pr ≤ PmaxR , (11e)

E(1)3 ≥ ξ, (11f)

where pcT and pcR are circuit power consumption, ξ is the minimum required energy harvested by U3,and φ1 and φ2 are the minimum required data rates for U1 and U2, respectively. Pmax

T and PmaxR are the

maximum power permitted at the transmitter and relay, respectively, to avoid interference with theprimary user.

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To guarantee that the power level from the transmitter and the relay will not interfere withthe primary user, the maximum transmission power at the transmitter and at the relay, respectively,are constrained as indicated in (12) and (13):

PmaxT = min

{Imax∣∣hTp∣∣2 , PT

}, (12)

where Imax is the power level of the maximum permissible interference with the primary user, PT is themaximum available power at the BS, and hTp is the channel coefficient from the secondary transmitterto the primary user; and:

PmaxR = min

{Imax∣∣gRp∣∣2 , PR

}, (13)

where gRp is the channel coefficient from the relay to the primary user, and PR is the maximumavailable power at the relay.

To solve problem (11), we propose a low-complexity algorithm based on PSO [15]. First, we definethe boundaries of the variables p1, p2, p3 and pr based on the constraints in problem (11).Then, the minimum transmit power for Message 1 is calculated based on (11b) and (11f), the minimumtransmit power of Message 2 at the transmitter is calculated based on (11c) and (11f), the minimumtransmit power intended for the EH user is calculated based on (11f), and the minimum transmitpower of the relay is calculated based on (11c), as follows:

p1 min = max

((22φ1 − 1

) σ21

h2Tu1

, α

), (14)

p2 min = max (γ1, γ2, α) , (15)

p3 min = max (0, α) , (16)

pr min = max (δ1, δ2) , (17)

in which γ1 =(22φ2 − 1

) p1 minhTR+σ2R

hTR, δ1 =

(22φ2 − 1

) σ2u2

g2Ru2

, γ2 =

(22φ2 − 1−

PmaxR gRu1

σ2u1

)p1 minhTu1

+σ2u1

hTu1,

δ2 =

(22φ2 − 1−

PmaxT hTu1

p1 minhTu1+σ2

u1

)σ2

u1gRu1

, and α = 2ξhTu3− 2Pmax

T .

The overall algorithm of the proposed scheme using PSO is described in Algorithm 1. Let Itmax,S, w, c1, and c2, respectively, denote the maximum number of iterations, the total number ofparticles, the inertia weight parameter, and the acceleration coefficients. Each particle’s positionrepresents a vector of four elements (p1, p2, p3, pr) for which the boundaries are

[p1 min, Pmax

T],[

p2 min, PmaxT

],[p3 min, Pmax

T]

and[pr min, Pmax

R], respectively. Let xn, vn, and pn

best define the position,velocity, and local best position of particle n, respectively.

In addition, the global best position of all particles is defined by gbest. We use a penalty functionto deal with the constraints, where we define fitness function f (xn) = f (p1, p2, p3, pr) based on theobjective function of problem (11), as follows:

f (xn) =Ru1 + Ru2

12 (p1 + p2 + p3 + pcT) +

12 (pr + pcR)

− ρ5

∑i=1

δ (gi), (18)

where ρ is the penalty value, gi is the i-th constraint of problem (11), and δ (gi) = 0 if gi is satisfied andδ (gi) = 1 otherwise. Note that if all the constraints are satisfied (feasible point), f (xn) is the objectivefunction (11a) without penalty.

Appl. Sci. 2020, 10, 3630 7 of 15

Algorithm 1: The proposed PSO algorithm to solve SEE problem (11).Data: Itmax, S, w, c1, c2 and variables {xn}.Initialize the positions of particles randomly xn = {p1, p2, p3, pr}, and evaluate f (xn).Find the index of the best particle: gbest = arg max

1≤n≤Nf (xn).

Define the initial local best position: pnbest = xn, ∀n.

Define the initial velocity of the particles: vn = 0, ∀n.for i = 1 : 1 : Itmax do

for each particle n = 1, . . . , S doCalculate random numbers: rn

1 , rn2 ∼ U (0, 1).

The velocity of the particle is updated as:vn ← wvn + c1rn

1(pn

best − xn)+ c2rn

2 (gbest − xn).Update particle’s position: xn ← xn + vn.Limit xn in their respective boundaries and get f (xn).Evaluate the local best position:if f (xn) > f

(pn

best)

thenpn

best ← xn

endEvaluate the global best position:if f (xn) > f (gbest) then

gbest ← xn

endend

endResult: Set f (gbest) as the maximum SSE of problem (11).

Under the presence of more users, the proposed system model can be utilized by applying a usergrouping scheme. For instance, a user grouping for a downlink NOMA system is proposed in [16].In the paper, the authors considered a grouping scheme where two users are selected for each group(strong user and weak user), and the different groups use orthogonal resources by avoiding interferencebetween groups. In [17], the authors proposed a NOMA-TDMA scheme by considering an uplinkindustrial IoT scenario composed of several sensors and one sink. The first step is to sort the channelgains and divide the total time into several time slots. Then, an optimization problem is formulated toallocate the power with NOMA and define the duration of the time slots, where the system allowsa maximum of two users in each group, and the different groups are assigned different time slots. Basedon the previous studies on many users, therefore we can group the users according to their channelgains, where each time slot is assigned to each group. In this case, there is no interference betweenusers in different groups, and an extension of the proposed scheme can be applied to allocate thepower to maximize the SEE with NOMA in each group. However, it is noteworthy that the proposedscheme considers that there is no direct link to the secondary user 2 because of path obstruction sothat a cooperative relay is needed to consider. In the case of a user grouping scheme, there exist somegroups where the distant secondary user has poor channel conditions. In that case, our proposedscheme based on a cooperative relay can be utilized efficiently.

In the case of multiple relays, the development of a relay selection algorithm is needed,where a simple solution is an exhaustive search among the possible relays. That is to say, we canperform the power allocation while considering each relay and choose the relay that achieves thehighest SEE. However, an efficient solution with multiple relays needs a joint optimization of the powervariables and relay selection, which may be topics for future research. On the other hand, the case ofmultiple eavesdroppers can be addressed by considering just the eavesdropper with the highest SINRto compute the secrecy rate with small modifications in (2) and (5), following the approach proposedin [18].

Appl. Sci. 2020, 10, 3630 8 of 15

4. Energy Efficiency Maximization in the Baseline CR-OMA Scheme with Cooperative Relayingand an EH User

In this section, we describe the baseline scheme for the energy efficiency maximization problemin OMA with cooperative relaying and an EH user. In OMA, the messages are sent to each user indifferent time slots. Accordingly, the transmission of each message from the transmitter to its respectivesecondary user in the OMA scheme involves three phases, which are detailed as follows.

In Phase 1, the transmitter sends message x1 to U1. Therefore, the rate of Message 1 at U1 can beexpressed as

Rx1,Tu1_OMA =13

log2(1 +p1hTu1

σ2u1

). (19)

The rate of Message 1 at the eavesdropper is:

Rx1,TE_OMA =13

log2(1 +p1hTE

σ2Ev

). (20)

Accordingly, the secrecy rate of Message 1 is given by

Ru1_OMA =[Rx1,Tu1_OMA − Rx1,TE_OMA

]+. (21)

In Phase 2, the transmitter sends Message 2 to the relay. Then, the rate of Message 2 at the relay isas follows:

Rx2,TR_OMA =13

log2(1 +p2hTR

σ2R

). (22)

In Phase 3, the relay forwards Message 2 to U2. Then, the rate of Message 2 at User 2 is

Rx2,Ru2_OMA =13

log2(1 +prgRu2

σ2u2

). (23)

The achievable rate for Message 2 is defined by the rate observed at U2 and the relay, as follows:

Ru2,min _OMA = min(Rx2,TR_OMA, Rx2,Ru2_OMA). (24)

The rate for Message 2 at the eavesdropper is given as follows:

Rx2,E_OMA =13

log2(1 +p2hTE

σ2E

+prgRE

σ2E

), (25)

Therefore, the secrecy rate of Message 2 is defined as:

Ru2_OMA =[Ru2,min _OMA − Rx2,E_OMA

]+. (26)

To improve the OMA scheme, the transmitter does not send an energy signal to User 3, because itinvolves an extra period of time to send that signal; instead, we assume that User 3 stores the energythat comes to U1 from the transmitter during Phase 1 plus the energy that comes from the transmitterto the relay during Phase 2. In that way, it is possible to take advantage of the energy used by thetransmitter when it sends the messages of secondary users. Accordingly, the energy stored by User 3 isgiven by

E3_OMA =hTu3

(p1 + p2

)3

. (27)

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Our goal is to maximize the secrecy energy efficiency, to guarantee the QoS requirement ofthe minimum rate at each secondary user, minimum requered energy and to guarantee maximumpermitted power at the relay and transmitter. Accordingly, the problem can be formulated as follows:

maxp1,p2,pr

Ru1_OMA + Ru2_OMA13 (p1 + pcT1) +

13 (p2 + pcT2) +

13 (pr + pcR1)

(28a)

s.t. Rx1,Tu1_OMA ≥ φ1, (28b)

Ru2,min _OMA ≥ φ2, (28c)

p1 ≤ PmaxT , (28d)

p2 ≤ PmaxT , (28e)

pr ≤ PmaxR , (28f)

E3_OMA ≥ ξ, (28g)

where pcT1, pcT2 and pcR1 are circuit power consumption during the phase 1, phase 2 and phase 3 atthe transmitter and at the relay, respectively,

Similar to the proposed solution to P1, secrecy energy efficiency maximization problem P2 forCR-OMA is solved by using the PSO algorithm. Therefore, we need to establish the boundaries forpower allocation variables p1, p2, and pr to be optimized. In this sense, the minimum transmit power,p1 min _OMA, is calculated based on constraints (28b) and (28g), with p2 min _OMA calculated based on(28c) and (28g), and with pr min _OMA calculated based on constraint (28c), as follows:

p1 min _OMA = max

((23φ1 − 1

) σ2u1

hTu1

, ω

), (29)

p2 min _OMA =

((23φ2 − 1

) σ2R

hTR, ω

), (30)

pr min _OMA =(

23φ2 − 1) σ2

u2

gRu2

, (31)

where ω = 3ξhTu3− Pmax

T .Accordingly, the boundaries of each particle’s position for the power allocation variables in the

PSO algorithm are[p1 min _OMA, Pmax

T],[p2 min _OMA, Pmax

T]

and[pr min _OMA, Pmax

R].

5. Simulation Results

In this section, we numerically evaluate the performance of our proposed PSO-based algorithmin the CR-NOMA network with cooperative relaying and an EH user, as illustrated in Figure 1,in comparison with the CR-OMA approach and with the baseline exhaustive search (ES) method.In the simulations, the channels are modeled as h̃Tu1 ∼ CN

(0, d−v

Tu1

), h̃Tu3 ∼ CN

(0, d−v

Tu3

), h̃TR ∼

CN(0, d−v

TR), h̃TE ∼ CN

(0, d−v

TE), g̃Ru1 ∼ CN

(0, d−v

Ru1

), g̃Ru2 ∼ CN

(0, d−v

Ru2

), g̃RE ∼ CN

(0, d−v

RE),

h̃Tp ∼ CN(

0, d−vTp

), and g̃Rp ∼ CN

(0, d−v

Rp

), where dij is the distance between device i and j, and the

path loss exponent is defined by v. We evaluated the proposed algorithm with the following parameters:v = 4, σ2 = −60 dBm, w = 0.7, and c1 = c2 = 1.494. The simulations were carried out on a computerwith 16 GB of RAM and an Intel Core i7-6700K CPU by using Matlab.

The distance from the transmitter to the EH user is set as dTu3= 10 meters. This distance needs to

be small since the RF signal is attenuated as the distance increases and there exists a minimum energyharvesting requirement. In addition, it is common to find in the literature distances of 10 m or less for

Appl. Sci. 2020, 10, 3630 10 of 15

an EH user. For instance, we can refer to [11], where the authors used a distance of four meters fromthe secondary BS to the secondary EH users.

On the hard, depending on the scenario, the distances of the secondary users can be small.For example, picocells consider a maximum range of 200 m [19]. In the literature, common distancesassumed to NOMA users are in the range of 10 to 80 m [2,6,20]. In addition, the objective of theproposed optimization problem is to maximize the SEE of the secondary network, which has relativelysmall distances since the transmission power is constrained with a maximum permissible interferencewith the primary users. In this paper, therefore we consider the distances from the secondarytransmitter to User 1, the relay, the PU, and the eavesdropper as dTu1

= 30, dTR = 50, dTp = 60,and dTE = 50 in meters, respectively. The distances from the relay to User1, User2, the PU, and theeavesdropper are defined as dRu1

= 30, dRu2= 50, dRp = 50 and dRE = 30 in meters, respectively.

With respect to the maximum permissible interference power with the PU, Tuan et al. [21] studiedthe effects of the maximum permissible interference power in a range from −30 dBm to −90 dBm.In addition, the trade-off between the interference power and throughput of the cognitive network wasinvestigated in [22], where the authors considered a range from−10 dBm to−40 dBm for the maximumpermissible interference power. It is noteworthy that as we increase the maximum interference powervalue, we obtain a wider feasible domain of the problem. Then, to analyze the worst scenario, we selectImax = −60 dBm.

To define the number of particles in the proposed PSO-based algorithm, we analyze the relativechange of the objective function, i.e., SEE, for several numbers of particles, S. The relative changecan be defined as

∣∣ f (gbest)i−1 − f (gbest)i∣∣/ f (gbest)i−1, where f (gbest)i−1 is the fitness function of the

global best particle at iteration i− 1 and f (gbest)i is the fitness function of the global best particle at thecurrent iteration i. We present in Figure 2 the relative change of the SEE when the number of particlesare equal to 25, 20 and 15, respectively. The values of the minimum rates at the secondary users areφ1 = φ2 = 1(bit/s/Hz), the minimum energy harvested by the EH user is ξ = −18 dBm, and thetransmit power at both the transmitter and the relay is PT = PR = 30 dBm. In addition, Table 2 showsthe comparison of a different number of particles when the number of iterations was selected to satisfya tolerance of 10−4 in the relative change of the SEE. The absolute error is evaluated by taking intoaccount the SEE obtained by exhaustive search. We can observe that the absolute error is very smallfor all the cases with a small value in the computational time. The case with S = 10 archives the lowestcomputational time, however, the small number of particles in PSO can lead to a local optimal solution,which should be avoided. Therefore, in the paper, we had selected S = 20 particles to be used in therest of the simulations.

10 20 30 40 50 60 70 80 90 100 110

Iteration Index

0

2

4

6

8

10

12

Re

lative

ch

an

ge

of

the

SE

E

S = 25

S = 20

S = 15

Figure 2. The relative change of the SEE versus the number of iterations in PSO.

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Table 2. Effects of the number of particles in PSO.

Number of Particles 30 25 20 15 10

N. of iterations 80 85 90 90 100Absolute error 6.25× 10−6 1.39× 10−5 3.13× 10−5 0.000353 0.001005Time (ms) 22.54316 20.96096 18.91602 13.08286 9.843146

Figure 3 shows the convergence behavior of the proposed algorithm given in Algorithm 1 foran average of several channel realizations. The value of the minimum rates at the secondary usersare φ1 = φ2 = 0.5, 1, 1.5 (bits/s/Hz), the minimum energy harvested by the EH user is ξ = −18 dBmand the maximum available transmission power at the transmitter and the relay is PT = PR = 30 dBm.We can see that the SEE is enhanced as the iteration index is increased, and its convergence reachesa stable value from iteration index 50. However, from Table 2, we observe that we need at least90 iterations to achieve a tolerance of 10−4. Then, we consider Itmax = 70 for further simulations,which is a trade-off between accuracy and computational time. We also observed that the SEE increaseswhen decreasing the minimum data rate requirement of the secondary users. The reason for this isthat the transmitter and the relay should deliver low transmission power to satisfy the low requiredrate of the secondary users. Consequently, the eavesdropper hardly trap the messages transmittedfrom the transmitter and the relay.

Note that if a lower computational time is needed, we can reduce the number of particles anditerations with a consequent reduction in the accuracy of the solution. For instance, at 40 iterations,the tolerance value is around 0.03 with an absolute error of around 0.0008 in the case of S = 20 andφ1 = φ2 = 1(bits/s/Hz).

10 20 30 40 50 60 70 80 90 100 110 120

Iteration Index

0.005

0.01

0.015

0.02

0.025

0.03

0.035

Obje

ctive function S

EE

(bps/J

oule

/Hz)

φ1=φ

2=0.5 (bits/s/Hz)

φ1=φ

2=1.0 (bits/s/Hz)

φ1=φ

2=1.5 (bits/s/Hz)

Figure 3. The convergence behavior of the proposed PSO-based algorithm with different minimumrates at the secondary users.

In this paper, we analyze the computational cost based on the number of equations that thePSO-based algorithm needs to compute in each iteration, where a detailed study of the operationsinvolved in each equation is omitted since it includes simple operations that just uses real values anddo not have matrix operations. In addition, it is assumed that the secondary transmitter has highcomputational capabilities.

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The computational cost for a complete iteration of the proposed PSO-based algorithm dependson the evaluation of the objective function and constraints in the problem (11), and the computationsneeded to update the velocity and position of the particles. First, from the problem (11), the algorithmneeds to evaluate the expressions of the rates and the energy harvested for the current particle position,which requires the evaluation of 10 equations involving just real numbers. To estimate the objectivefunction and constraints, it is also necessary to evaluate 8 equations and one additional equationfor obtaining the fitness function in (18). Second, for each particle, we require to calculate tworandom numbers and evaluate 8 equations for the velocity update and position update since we havefour variables. Third, we limit the position of the particle and find the local and best positions bycomputing six equations. Then, for each particle n, we need to execute around 35 equations. Since thealgorithm repeats the process for a total of Itmax iterations, the total number of equations to beevaluated is 35× S× Itmax, which can be mathematically expressed as the computational complexityof O (S× Itmax).

In the case of the exhaustive search method, the complexity depends on the range of the variableswhich is based on numerical precision. Let us define ζ as the steps used for the power variables,

then the total possible values for the variable p1 are Υp1 =⌊(

PmaxT − p1 min + ζ

)/ζ

⌋, where the same

procedure is applied to the other variables to obtain Υp2 , Υp3 and Υpr . Then, for the ES method,we need to evaluate the objective function and constraints a total number of Υp1 × Υp2 × Υp3 × Υpr

times. We can observe that the proposed PSO-based scheme permits a huge reduction in thecomputational complexity compared with the exhaustive search. For instance, in the case ofφ1 = φ2 = 1(bits/s/Hz) and ξ = −18 dBm with a step of ζ = 1, the computational time of ES isaround 72,4492 (s), which increases exponentially by reducing the value of ζ, i.e., with more numericalprecision. By contrast, the PSO-based algorithm achieves a computational time of 18.92 (ms) witha number of particles equal to 20 and 90 iterations as we can see in Table 2.

Figure 4 shows a comparison of SEE performance between our proposal using NOMA and theconventional OMA scheme in accordance with the SEE objective function versus the minimum data rateat the secondary users when the minimum energy harvested by the EH user is ξ = −15 dBm, when themaximum available transmission power at the transmitter and the relay is PT = PR = 30 dBm.From Figure 4, we can see that the NOMA scheme significantly outperforms the traditional OMA.This is because, under NOMA, the location of both users is exploited to simultaneously transmitto User 1 and User 2, in which the power allocated for the distant user is higher, compared to thepower allocated for the closer user. This strategy is complemented with SIC in which the closeruser first decodes the message of the distant user, where the SINR is high since it has the higherpower, and it then subtracts that contribution to easily decode its own message (the message forthe closer user). For the distant user, the interference from the message of the closer user is low,since the power allocated to this message is not high. On the other hand, the OMA scheme does notuse SIC and the transmitter needs different periods of time to send each message to each intended user.Then, the transmission under the NOMA scheme is completed in two phases, as shown in Figure 1,while the transmission under OMA is completed in three phases. Therefore, because NOMA uses theresources more efficiently, it achieves better performance than the OMA scheme.

Moreover, we can see that the result obtained by our proposed PSO-based method achievesperformance very close to that obtained by the exhaustive search method, but with lower complexity.The reason is that the PSO-based method iteratively updates the global and local particles’ positions tosearch for the optimal solution, instead of systematically evaluating all possibilities to find its optimalsolution, as the exhaustive search method does.

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Figure 4. SSE performance comparison between the exhaustive search method, CR-NOMA withcooperative relaying, and CR-OMA with cooperative relaying, based on the minimum data raterequirements for the secondary users.

Figures 5 and 6 show that the proposed CR-NOMA scheme outperforms the baseline OMAscheme, and this finding confirms the outcomes obtained in the simulation results seen in Figure 3.From Figure 5, we can see that the SEE decreases when increasing the minimum required harvestedenergy at User 3. This is because the transmitter needs to send more power to satisfy the requirementof the EH user, and this fact requires p3 to increase, which is inversely proportional to the maximizationof the objective function (11a). Moreover, as the values of the data rate requirement increase, the SEEperformance decreases, since more power must be delivered by the transmitter and the relay inorder to satisfy the data rate requirements, which makes it easier for the eavesdropper to catch themessages. Figure 6 shows a comparison of SEE performance between our proposal using NOMAversus the minimum energy harvested by User 3 when the minimum data rates at the secondaryusers are φ1 = φ2 = 0.5, 1, 1.5 (bit/s/Hz), when the maximum available transmission power at thetransmitter and the relay is PT = PR = 30 dBm. From Figure 6, we verify that the performance underNOMA is superior to OMA, and we can see that when the values of energy harvested and for datarate requirements increase, the values of the SEE start to decay.

Figure 5. SSE performance comparison between CR-NOMA and CR-OMA according to the minimumharvested energy at User 3 and the minimum rates at secondary User 1 (φ1) and secondary User 2 (φ2).

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Figure 6. SSE performance comparison between CR-NOMA and CR-OMA according to the minimumharvested energy at User 3 with three different values for the data rate requirements at secondaryUser 1 (φ1) and secondary User 2 (φ2).

6. Conclusions

This paper proposes a low-complexity PSO-based algorithm to maximize the SEE in a cooperativerelay CR-NOMA network with an EH user. The power allocation variables for each user are optimizedto achieve SEE maximization under the following constraints: a minimum data rate for secondaryusers, a minimum level of harvested energy for the EH user, and the maximum permitted transmissionpower at both the secondary transmitter and the relay (based on a threshold for interference withthe primary user). To validate the outcomes of the proposed solution, we compared the performanceof our proposed PSO-based algorithm with the exhaustive search method. We confirmed that PSOachieves near-optimal performance compared to that obtained by the high computational–complexityexhaustive search method. Moreover, we studied SEE maximization in a cooperative relaying CR-OMAnetwork with an EH user and compared it with our proposed scheme using the NOMA transmissionstrategy. The experimental results confirm the advantage of the proposed NOMA method comparedto the OMA scheme, where an improvement in the SEE of around 40% to more than 100% is achievedby NOMA compared with OMA in the scenario varying the minimum energy harvested at user 3.

Author Contributions: C.E.G. conceived and proposed the research idea. All authors designed the experiments.C.E.G. performed the experiments. M.R.C. and I.K. analyzed the experimental results. C.E.G. wrote the paperunder the supervision of I.K. All authors have read and agreed to the published version of the manuscript.

Funding: This research was supported by the National Research Foundation of Korea (NRF) through the KoreanGovernment and the Ministry of Science and ICT (MSIT) under Grant NRF-2018R1A2B6001714.

Conflicts of Interest: The authors declare no conflict of interest.

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